| utf31-002 Find the volumes of the following solids using calculus.
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| utf31-003 Find the volume of the following solids obtained by rotating:
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| utf31-004 Derive the volumes for the following solids.
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| utf31-005 Since El Paso is such a long way from Austin, Tasha and Olivia decide to make a little money for a flight home by helping out a local painter. The painter had always been fond of the curve $y=\frac{1}{ x}$ and wanted them to engineer a paint can utilizing his favorite curve. They decide create a paint can by revolving the curve $y=\frac{1}{ x}$ from $x=1$ to $x=H$ about the x-axis.
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| utf35-001 Work out the following integrals. \begin{alignat*}{2} &a) \int{\frac{7}{ (x-2)(x+5)}} & &b) \int{\frac{e^{{2x}} - e^x }{ e^x + 1}} \\ &c) \int{\frac{x^5-x^4-3x^3-2x^2+2x+5 }{ x^4 + x^3}}& &d) \int{\frac{x^2-7x+9 }{ x^3-3x+2}}\\ &e) \int{\frac{dx }{ x^4-16}} & &f) \int{\frac{x^4+7x^3-5x^2+13x-10 }{ (x^2+2x+3)(x-1)^2}}\\ &g) \int{\frac{5x^2+7x+2 }{ x^3+2x^2-2x+3}} & &h) \int{\frac{dx }{ (x^2 + 16)^2}} \\ &i) \int{\frac{2x^4+x^3+7x^2+2 }{ x^5+2x^3+x}} \end{alignat*} |